4 versions = 4 separate versions of the game available for PS2. DDRMax, DDRMax2, DDR Extreme, and DDR Extreme 2.
Extreme 2 was just released in the last couple months and can easily found bundled with a dance pad. It should be about $60. The other games can be found for about $30 (maybe the older ones can be found for $20, not sure though)
I actually bought the Mario version for the Gamecube for myself (I grew up on Nintendo, and will always be a Nintendo kid) and yes it is the only version of DDR for the 'Cube. And while it uses Mario to grab onto a yonuger audience, the songs in hard and super hard mode are quite difficult for me, lol.
The DDR games don't NEED an eye toy in order to play, but Extreme 1 and Extreme 2 include mini-games that are compatible with the eyetoy (and the games do not come with it, but like I said, its not mandatory.)